Who am I?
I am a full professor in Pitt's math department.
My research is mainly in numerical analysis.
Numerical analysis is one of the broadest areas
of mathematics as it includes convergence
questions of analysis, including new convergence
issues related to the rate of convergence,
problems of mechanics, nonlinear PDEs and applications
across the spectrum of mathematics to graph theory.
I've worked in all these areas and a number of others too,
authoring more than
160-odd refereed publications, 1 undergrad text, 1 grad text and 2
research monographs.
Through all this variety I have had an
abiding fascination with the deep mathematics of fluid motion,
which, paraphrasing, is an area of mathematics in which

"a gnat may
bathe and an elephant may drown."

I've had approaching 40 PhD students almost all of whom are active
and
accomplished researchers.
My PhD students now direct PhD students who are themselves doing
very well.
I've directed a number of MS students who wrote excellent theses and
I've advised undergrad researchers who did
terrific work and moved forward to great things.

Outside of mathematics my other interests have been quite varied.
I was chess champion of Georgia in 1976 and
played various sports over time. I am currently an avid mid-level
whitewater kayaker. I get many mathematical ideas
from observations of turbulent flows in nature!

I also have had a number of PhD students visiting from other countries
and other advisors:
(a partial list of recent ones)
Lars Roehe
(2 months), Li Shen, Haibiao Zheng, Yao Rong and Osman Isik
(all for the full year).
These visits to our academic family here have been happy and productive!

*New Models and Algorithms for Complex Turbulence, e.g., turbulence
not at statistical equilibrium.
This project
involves developing models with a rigorous mathematical foundation
as well as numerical analysis of new methods for their solution.

* Ensemble Simulation Models and Algorithms for Turbulence. A joint
project with Nan Jiang.
Ensemble simulations are necessary for extending forecast skill,
dealing with errors from unknown data and parameterizations and
estimating sensitivities. However, they lead to the inevitable
conflict
of high resolution single realizations and computing ensembles.
We have new methods breaking this deadlock. The new methods lead
to new models as well since ensemble data gives a simple
and calculable way to specify, WITHOUT MODELLING, the TKE.
We have also developed a NEW MIXING LENGTH which seems to
correct the inadequacies of standard mixing length theories.
* Partitioned time stepping methods for coupled, multi domain &
physics:
Atmosphere-Ocean coupling in climate models,
multi-physics coupling, e.g., NSE & Maxwells eqns in MHD,
Fully evolutionary Stokes-Darcy-Biot coupling.
*Large Eddy Simulation -
LES reports.
Modern LES models in complex applications and legacy codes
including VMS methods, Nonlinear filters, Approximate deconvolution
models.

*Uncertainty Quantification. A joint project with Clayton Webster
at ORNL and Catalin Trenchea
at Pitt.
We are interested in improving current approaches, developing new ones
and
and studying the interplay between numerical and modelling errors in
turbulence.

*The BigData in turbulent combustion project.
This is a new collaboration including Alexandros Labrinidis, Peyman
Givi,
Panos Chrysanthis and Patrick Pisciuneri.
*Algorithms for Flow in complex pebble bed geometries in which
geometric complexity cannot be resolved.

*Long Time Behavior of Numerical Methods.
Click for LTB.A long time interest of mine!

* Energy Transfer theories of turbulence and shell
models. I work on these to let undergrads get involved in research on
turbulent flows. There are a lot of interesting conjectures that can
be
interrogated via shell and ET Models.

My personal preference is to work on problems
where mathematics can make a difference in extending
the boundary of what is predictable rather than perfecting
a theory where the main outlines are already known.
(There is nothing wrong in the latter. Math is hard enough that
progress will only be possible when we all work on whatever is
closest to our own hearts.)

In all these areas, one common theme is:
Mathematical analysis as a guide to practical computation.

*Jeff Connor,
PhD 2010, Uncoupling Ocean--Atmosphere models
Jeff completed his PhD in 4 years and wrote one of the most consequential PhD theses of our department.
Jeff was a postdoc at LLNL and is now a tenure track Asst. Prof at U Conn,
Avery Point.

*Alex Lozovskiy,
PhD 2010, Alex opened a new area of computational science up to rigorous numerical analysis:
Prediction and modelling of the noise
generated by
turbulence
Alex is now a postdoc at Texas A&M and will be moving to industry soon..

*Nate Mays, Nate was a tenure track Asst Prof at WJU and will be joining EPIC in
Fall 2014.
High accuracy methods for ill-posed
problems and applications to an biomedical parameter identification problem with diagnostic implications.

*Ross Ingram,
Numerical analysis of discrete Brinkman models for porous media flow. Ross'
web page. Ross is a leader in an industrial research group at
Bettis since fall 2011.

*Sara Hritz,MS 2010, Phenomenology and Computations
of a Regularization of the Navier-Stokes equations related to a
Non-Newtonian fluid model, currently: Scientific Analyst, UPMC.

* A. Sunmonu,
Ph.D. 1992,
"Numerical Analysis of Nonlinear Models of Electrically and Thermally
Conducting Materials"
Currently: Full Professor and Dept Chairman,
Department of Mathematics and Computer Science,
City University of New York- York A.Sunmonu's
web page.

* F.Fairag,
Ph.D., 1998,
"A two-level discretization method for the stream-function form of the
Navier-Stokes equations"
Associate Professor,
Department of Mathematics, King Fahd University of Petroulem and Minerals
F.Fairag's
web page.

[2] M. Anitescu and G.Hart,
A constraint-stabilized time-stepping approach for rigid multibody
dynamics with joints, contact and friction.
Preprint ANL/MCS-1002-1002. Submitted to International Journal for
Numerical Methods in Engineering.

[3] M. Anitescu and G. Hart. A Fixed-Point Iteration Approach for Multibody Dynamics with Contact
and
Small Friction.
Preprint ANL/MCS-P985-0802. To appear in Mathematical Programming
Series
B.,2003.

[4] M. Anitescu, A. Miller and G. Hart. Constraint stabilization for time-stepping approaches for rigid
multibody
dynamics with joints, contact and friction.
Preprint ANL/MCS-P1023-0203. To appear in the Proceedings of the
Annual
Conference of the American Society of Mechanical Engineers, 2003.

[5] G. Hart and Mihai Anitescu. A hard constraint time-stepping approach for multibody dynamics with
contact and friction.
To appear in the Proceedings of the Tapia Conference for Diversity in
Computing, 2003.

Other Scientific Intrests:
I've worked in several related areas and I still have research
interests
in these areas. In no particular order, some of these other areas
in which I've written a few papers include:

*Parallel Algorithms for Highly Nonsymmetric Problems -we have
developed massively data parallel algorithms for solving linear and
nonlinear systems
arising from convection dominated phenomena. We have in particular
developed an element wise data parallel solution method which is
proven
to converge uniformly in the Peclet number.